Question

QUESTION # 1

The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1,264

1,278

1,208

1,250

1,268

1,316

1,275

1,317

1,275

(a)

Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x= ________-A.D.s= yr

(b)Find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site. Round your answers to the nearest whole number.

lower limit__________ A.D

.upper limit__________ A.D.

QUESTION # 2

What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):

56.9

55.5

53.2

65.5

59.0

64.7

70.1

64.7

53.5

78.2

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean percentage x and the sample standard deviation s. (Round your answers to one decimal place.)

x =	_______%
s =	_______%

(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

lower limit	_______ %
upper limit	_______%

Answer 1

1. a)  $\bar{x} = 1272$ A.D

$s= 33$ yr

b) Critical value $t_{c}= t_{8,0.1/2}= 1.860$

Margin of error, E = $t_{c}\frac{s}{\sqrt{n}}$ =  $1.860\frac{33}{\sqrt{9}}$ = 20.46

Lower Limit = $\bar{x} - E= 1272 - 20.46 = 1251$ A.D

Upper Limit = $\bar{x} + E= 1272 + 20.46= 1292$ A. D

2. a)  $\bar{x} = 62.1$ %

$s= 8.0$ %

b) Critical value $t_{c}= t_{9,0.1/2}= 1.833$

Margin of error, E = $t_{c}\frac{s}{\sqrt{n}}$ =  $1.833\frac{8.0}{\sqrt{10}}$ = 4.6

Lower Limit = $\bar{x} - E= 62.1 -4.6 = 57.5$ %

Upper Limit = $\bar{x} - E= 62.1 +4.6 = 66.7$ %